Question

Time for $20$ oscillations of a pendulum is measured as ${{\text{t}}_1} = 39.6{\text{s}}$, ${{\text{t}}_2} = 39.9{\text{s}}$ and ${{\text{t}}_3} = 39.5{\text{s}}$. What is the precision in the measurements? What is the accuracy of measurement?

Answer 1

Error measurement: Every instrument used for measurement has some errors; it may be due to some physical changes like temperature and composition of the materials.
Precession: It is a description of random errors, a measure of statistical variability.
Accuracy: It is the quantity to determine how close a measurement is to the correct value for that measurement.
The accuracy is classified into three types such as point accuracy, accuracy as percentage scale range, accuracy as the percentage of true value. Point accuracy is defined as the accuracy of the instrument only at a particular point on its scale. Accuracy as a percentage scale range is defined as the uniform scale range that determines the accuracy of measurement on its scale. Accuracy as a percentage of true value: It is determined by identifying the measured value regarding their true value.

Formula used:
${\text{Mean value = }}\dfrac{{({\text{sum of all the terms)}}}}{{({\text{no}}{\text{. of terms)}}}}$, {\text{% Error measurement = }}\dfrac{{{\text{Error value}}}}{{{\text{True value}}}} \times {\text{100}}
${\text{Error value = True value - Measured value}}$

Complete step by step solution:
Given details, ${{\text{t}}_1} = 39.6{\text{s}}$,${{\text{t}}_2} = 39.9{\text{s}}$, ${{\text{t}}_3} = 39.5{\text{s}}$ and the number of oscillations, ${\text{n = 20}}$
It is observed that the least count by the water is $0.1{\text{s}}$.
Measurements have only one decimal place so, precession measurement= least count of measuring instrument=$0.1{\text{s}}$
Therefore, precession in 1 oscillation is calculated as, $\dfrac{{0.1}}{{20}} = 0.005$

Hence, the correct precession is $0.005$.

Note: There are the following types of measurement:
Constant error: The error which affects each observation with the same amount
Systematic error: The error occurs in one direction, either in a positive or in a negative direction.
Instrumental error: The error that occurs due to the defect in the instrument.
Personal error: The error that occurs due to individual bias.
External error: The error that occurs due to the external changes.
Random error: The error that occurs due to the random changes in direction or magnitude.